Overview
- Addresses the latest developments in the field
- Provides comprehensive references to classic papers as well as the most recent literature
- Includes in-depth, essay-length chapters on key topics
Part of the book series: Encyclopedia of Complexity and Systems Science Series (ECSSS)
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Table of contents (25 entries)
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Front Matter
Keywords
- Invariant measure
- ergodic transformation
- weak mixing
- mixing
- ergodic theorem
- recurrence
- Koopman operator
- spectral measure
- K-transformation
- Bernoulli transformation
- entropy
- M{\"o}bius disjointness
- Sarnak conjecture
- Gaussian system
- Poisson suspension
- joining
- distal system
- Diophantine analysis
- nonsingular system
- Krieger's type
About this book
Editors and Affiliations
About the editors
Cesar E. Silva is the Hagey Family Professor of Mathematics at Williams College, where he has taught since 1984, and was chair of the department in 2008-2009 and 2010-2012. He received his PhD from the University of Rochester under the supervision of Dorothy Maharam, and his BS from the Pontificia Universidad Catolica in Peru. He has held visiting positions at a number of universities including Maryland and Toronto. In 2015, Silva was elected a Fellow of the American Mathematical Society. Silva’s research interests are in ergodic theory and dynamical systems, in particular the dynamics of nonsingular and infinite measure-preserving transformations, rank-one transformations, and p-adic dynamics. Silva is the author of Invitation to Ergodic Theory and Invitation to Real Analysis, both published by the American Mathematical Society, and is co-editor of two volumes of conference proceedings, published in the AMS Contemporary Mathematics series. He was associate editor of AMS Notices and is the author or co-author of over 50 research articles in the general area of ergodic theory.
Dr. Alexandre I. Danilenko is currently a leading research fellow at B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine. He is an expert in ergodic theory and dynamical systems. Dr. Danilenko conducts research in spectral theory, orbit theory, entropy theory, theory of joinings, nonsingular dynamics, topological dynamics, etc. During his career, he has authored or co-authored more than 60 research papers published in internationally recognized mathematical journals. Alexandre I. Danilenko received his C.Sc. degree in mathematics at Kharkiv State University in 1991 under the supervision of V. Ya. Golodets. More than 10 years he was employed as Assistant Professor and Associate Professor atV. Karazin Kharkiv National University (Ukraine). He habilitated at N. Copernicus University in Torun (Poland) in 2003. Since 2002 he has been working at B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine.
Bibliographic Information
Book Title: Ergodic Theory
Editors: Cesar E. Silva, Alexandre I. Danilenko
Series Title: Encyclopedia of Complexity and Systems Science Series
DOI: https://doi.org/10.1007/978-1-0716-2388-6
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Reference Module Computer Science and Engineering
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2023
Hardcover ISBN: 978-1-0716-2387-9Published: 01 August 2023
eBook ISBN: 978-1-0716-2388-6Published: 31 July 2023
Series ISSN: 2629-2327
Series E-ISSN: 2629-2343
Edition Number: 1
Number of Pages: XXII, 672
Number of Illustrations: 15 b/w illustrations, 35 illustrations in colour
Topics: Dynamical Systems and Ergodic Theory, Statistical Physics and Dynamical Systems, Theoretical and Applied Mechanics